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alexandr1967 [171]
2 years ago
11

Which value, to the nearest tenth, is the smallest solution of f(x) = g(x) if f(x) = ln(x + 5) – 1 and g(x) = x3 – 2x + 1?

Mathematics
1 answer:
nekit [7.7K]2 years ago
5 0

Answer:

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of x has the smallest distance with respect to origin: (x_{2},y_{2}) = (0.18,0)

(ii) The smallest solution is the most negative value: (x_{1},y_{1}) = (-1.577,0)

Step-by-step explanation:

Let f(x) = g(x), f(x) = \ln (x+5)-1 and g(x) = x^{3}-2\cdot x + 1, then we have the following implicit equation:

\ln (x+5)-x^{3}+2\cdot x -2 = 0 (1)

This equation cannot be solved by analytical means. There are two different strategies to solve this expression: (i) Numerical methods, (ii) Graphical methods. We decide to use the second method:

Let suppose that we use this function h(x) = \ln (x+5) -x^{3}+2\cdot x - 2. By the help of a graphing tool, we find the smallest solution such that h(x) = 0. There are three possible solutions: (x_{1},y_{1}) = (-1.577,0), (x_{2},y_{2}) = (0.18,0), (x_{3}, y_{3}) = (1.376, 0)

There are two possibilities of determine which solution is the smallest one:

(i) The smallest solution is the value of x has the smallest distance with respect to origin: (x_{2},y_{2}) = (0.18,0)

(ii) The smallest solution is the most negative value: (x_{1},y_{1}) = (-1.577,0)

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